"I'm just pointing out that it is a transfer of wealth from taxpayer to tenant"
Do you mean council housing or housing benefit?
When housing benefit is paid for social housing, the money is going back to the tax payer, no transfer of wealth there.
Or if you're talking about council housing, when a tenant gets a cheaper rent than a private property, all that means is that they are getting a better deal. It's not a transfer of wealth.
The big transfer of wealth is housing benefit to private LLs. That's a scandal IMO.
Why do you see the market rate as the "real" value btw?
A government LL is different to a private LL. If they don't house people, there are all sorts of other costs they must bear as a result of people being homeless. A private LL doesn't have to worry about these costs. As well as making money directly from the social housing schemes, governments / the tax payer save money when their population is properly housed (as the population generally have better health, don't need emergency housing, have better prospects and so pay more tax, commit fewer crimes etc).
A government must take all sorts of things into account to find the "real" value of something. The market value is something an investor can take as a yardstick for whether something is a good investment for them. Not so a government, they have to look at a much bigger picture to get the "real" value to the tax payer.